In one prior art circuit of a digital-to-analog conversion, a digital signal is firstly converted into a pulse width signal varying in its pulse width in response to its digital data value, and thereafter it passes through a smoothing filter to be demodulated into an analog signal. According to the prior art, a high precision of conversion can be obtained without any component of high precision.
However, in the prior art, since the pulse width of the pulse width signal varies, with the leading edge of the pulse starting at a periodic sampling time, the center of the pulse width varies in accordance with the data value of the sampled digital data. Therefore, the waveform of the demodulated analog signal disadvantageously differs from the waveform of the original analog signal. The portion of the demodulated analog signal in which a level increases is extended in comparison to the corresponding portion of the original analog signal while a portion of the demodulated analog signal in which a level decreases is compressed in comparison to the corresponding portion of the original analog signal. This gives second harmonic distortion.
In order to solve a problem of distortion, as shown in FIG. 1, it will be considered that a digital signal is converted into a pulse width signal P so that each of the pulses P.sub.a, P.sub.b, P.sub.c --varies in its pulse width in response to each respective data value of a corresponding sampled digital data and with the center of each pulse width having a constant time interval t.sub.0 from each sampling time t.sub.a, t.sub.b, t.sub.c --responsive to a sampling signal having a repetitive sampling period T. In this method, however, there will remain a distortion in the waveform of the demodulated analog signal as described later. In FIG. 2A, provided that sampling times are t.sub.1 through t.sub.8 when an original analog signal S is sampled by the sampling signal having a frequency eight times that of the sinewave signal, analog data sampled at each sampling time t.sub.1 through t.sub.8 is converted into corresponding digital data by an analog-to-digital conversion. The aforementioned digital signal-to-pulse width signal conversion is executed when these digital data are demodulated into the analog signal by a digital-to-analog conversion. In FIG. 2B, the digital data having varying pulse width values are shown as a pulse width signal P.sub.x having the center of each pulse width at each sampling time t'.sub.1 through t'.sub.8. This, for example, could be that digital signal obtained from the playback of a digital tape on which has been recorded the digital signal after analog-to-digital conversion of the original analog signal S shown in FIG. 2A. It will be considered that each pulse of the pulse width signal P.sub.x is a mixture of a pulse of a pulse width signal P.sub.y, produced when the zero reference level of the original analog signal is sampled, and a pulse of a pulse width signal P.sub.z produced by converting digital data corresponding to each level difference between a zero reference level and an actual sampled level of the original analog signal S.
Thus, when the pulse width signal P.sub.x is smoothed through a filter, the component of the demodulated analog signal corresponding to the pulse width signal P.sub.y has no distortion, but the component corresponding to the pulse width signal P.sub.z has a distortion of second harmonic wave H as shown in dotted lines D of FIG. 2A because the positive and negative pulses adjacent to the top and bottom of the original analog waveform are not symmetrical to each other.